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Preface

In the last two decades, there has been a tremendous surge of activity in robotics, both at in terms of research and in terms of capturing the imagination of the general public as to its seemingly endless and diverse possibilities. This period has been accompanied by a technological maturation of robots as well, from the simple pick and place and painting and welding robots, to more sophisticated assembly robots for inserting integrated circuit chips onto printed circuit boards, to mobile carts for parts handling and delivery. Several areas of robotic automation have now become “standard” on the factory floor and, as of the writing of this book, the field is on the verge of a new explosion to areas of growth involving hazardous environments, minimally invasive surgery, and micro electro-mechanical mechanisms.

Concurrent with the growth in robotics in the last two decades has been the development of courses at most major research universities on various aspects of robotics. These courses are taught at both the undergraduate and graduate levels in computer science, electrical and mechanical engineering, and mathematics departments, with di erent emphases depending on the background of the students. A number of excellent textbooks have grown out of these courses, covering various topics in kinematics, dynamics, control, sensing, and planning for robot manipulators.

Given the state of maturity of the subject and the vast diversity of students who study this material, we felt the need for a book which presents a slightly more abstract (mathematical) formulation of the kinematics, dynamics, and control of robot manipulators. The current book is an attempt to provide this formulation not just for a single robot but also for multifingered robot hands, involving multiple cooperating robots. It grew from our e orts to teach a course to a hybrid audience of electrical engineers who did not know much about mechanisms, computer scientists who did not know about control theory, mechanical engineers who were suspicious of involved explanations of the kinematics and dynamics of garden variety open kinematic chains, and mathematicians who were curious, but did not have the time to build up lengthy prerequisites before

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beginning a study of robotics.

It is our premise that abstraction saves time in the long run, in return for an initial investment of e ort and patience in learning some mathematics. The selection of topics—from kinematics and dynamics of single robots, to grasping and manipulation of objects by multifingered robot hands, to nonholonomic motion planning—represents an evolution from the more basic concepts to the frontiers of the research in the field. It represents what we have used in several versions of the course which have been taught between 1990 and 1993 at the University of California, Berkeley, the Courant Institute of Mathematical Sciences of New York University, the California Institute of Technology, and the Hong Kong University of Science and Technology (HKUST). We have also presented parts of this material in short courses at the Universit`a di Roma, the Center for Artificial Intelligence and Robotics, Bangalore, India, and the National Taiwan University, Taipei, Taiwan.

The material collected here is suitable for advanced courses in robotics consisting of seniors or firstand second-year graduate students. At a senior level, we cover Chapters 1–4 in a twelve week period, augmenting the course with some discussion of technological and planning issues, as well as a laboratory. The laboratory consists of experiments involving on-line path planning and control of a few industrial robots, and the use of a simulation environment for o -line programming of robots. In courses stressing kinematic issues, we often replace material from Chapter 4 (Robot Dynamics) with selected topics from Chapter 5 (Multifingered Hand Kinematics). We have also covered Chapters 5–8 in a ten week period at the graduate level, in a course augmented with other advanced topics in manipulation or mobile robots.

The prerequisites that we assume are a good course in linear algebra at the undergraduate level and some familiarity with signals and systems. A course on control at the undergraduate level is helpful, but not strictly necessary for following the material. Some amount of mathematical maturity is also desirable, although the student who can master the concepts in Chapter 2 should have no di culty with the remainder of the book.

We have provided a fair number of exercises after Chapters 2–8 to help students understand some new material and review their understanding of the chapter. A toolkit of programs written in Mathematica for solving the problems of Chapters 2 and 3 (and to some extent Chapter 5) have been developed and are described in Appendix B. We have studiously avoided numerical exercises in this book: when we have taught the course, we have adapted numerical exercises from measurements of robots or other “real” systems available in the laboratories. These vary from one time to the next and add an element of topicality to the course.

The one large topic in robotic manipulation that we have not covered in this book is the question of motion planning and collision avoidance

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for robots. In our classroom presentations we have always covered some aspects of motion planning for robots for the sake of completeness. For graduate classes, we can recommend the recent book of Latombe on motion planning as a supplement in this regard. Another omission from this book is sensing for robotics. In order to do justice to this material in our respective schools, we have always had computer vision, tactile sensing, and other related topics, such as signal processing, covered in separate courses.

The contents of our book have been chosen from the point of view that they will remain foundational over the next several years in the face of many new technological innovations and new vistas in robotics. We have tried to give a snapshot of some of these vistas in Chapter 9. In reading this book, we hope that the reader will feel the same excitement that we do about the technological and social prospects for the field of robotics and the elegance of the underlying theory.

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Acknowledgments

It is a great pleasure to acknowledge the people who have collaborated with one or more of us in the research contained in this book. A great deal of the material in Chapters 2 and 3 is based on the Ph.D. dissertation of Bradley Paden, now at the University of California, Santa Barbara. The research on multifingered robot hands, on which Chapters 5 and 6 are founded, was done in collaboration with Ping Hsu, now at San Jose State University; Arlene Cole, now at AT&T Bell Laboratories; John Hauser, now at the University of Colorado, Boulder; Curtis Deno, now at Intermedics, Inc. in Houston; and Kristofer Pister, now at the University of California, Los Angeles. In the area of nonholonomic motion planning, we have enjoyed collaborating with Jean-Paul Laumond of LAAS in Toulouse, France; Paul Jacobs, now at Qualcomm, Inc. in San Diego; Greg Walsh, Dawn Tilbury, and Linda Bushnell at the University of California, Berkeley; Richard Montgomery of the University of California, Santa Cruz; Leonid Gurvits of Siemens Research, Princeton; and Chris Fernandez at New York University.

The heart of the approach in Chapters 2 and 3 of this book is a derivation of robot kinematics using the product of exponentials formalism introduced by Roger Brockett of Harvard University. For this and manifold other contributions by him and his students to the topics in kinematics, rolling contact, and nonholonomic control, it is our pleasure to acknowledge his enthusiasm and encouragement by example. In a broader sense, the stamp of the approach that he has pioneered in nonlinear control theory is present throughout this book.

We fondly remember the seminar given at Berkeley in 1983 by P. S. Krishnaprasad of the University of Maryland, where he attempted to convince us of the beauty of the product of exponentials formula, and the numerous stimulating conversations with him, Jerry Marsden of Berkeley, and Tony Bloch of Ohio State University on the many beautiful connections between classical mechanics and modern mathematics and control theory. Another such seminar which stimulated our interest was one on multifingered robot hands and cooperating robots given at Berkeley in 1987 by Yoshi Nakamura, now of the University of Tokyo. We have also

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enjoyed discussing kinematics, optimal control, and redundant mechanisms with John Baillieul of Boston University; Je Kerr, now of Zebra Robotics; Mark Cutkosky of Stanford University and Robert Howe, now of Harvard University; Dan Koditscheck, now of the University of Michigan; Mark Spong of the University of Illinois at Urbana-Champaign; and Joel Burdick and Elon Rimon at the California Institute of Technology. Conversations with Hector Sussmann of Rutgers University and Gerardo La eriere of Portland State University on nonholonomic motion planning have been extremely stimulating as well.

Our colleagues have provided both emotional and technical support to us at various levels of development of this material: John Canny, Charles Desoer, David Dornfeld, Ronald Fearing, Roberto Horowitz, Jitendra Malik, and “Tomi” Tomizuka at Berkeley; Jaiwei Hong, Bud Mishra, Jack Schwartz, James Demmel, and Paul Wright at New York University; Joel Burdick and Pietro Perona at Caltech; Peter Cheung, Ruey-Wen Liu, and Matthew Yuen at HKUST; Robyn Owens at the University of West Australia; Georges Giralt at LAAS in Toulouse, France; Dorothe` Normand Cyrot at the LSS in Paris, France; Alberto Isidori, Marica Di Benedetto, Alessandro De Luca, and ‘Nando’ Nicol´ at the Universit`a di Roma; Sanjoy Mitter and Anita Flynn at MIT; Antonio Bicchi at the Universit`a di Pisa; M. Vidyasagar at the Center for Artificial Intelligence and Robotics in Bangalore, India; Li-Chen Fu of the National Taiwan University, Taipei, Taiwan; and T.-J. Tarn of Washington University. Finally, we are grateful to Mark Spong, Kevin Dowling, and Dalila Argez for their help with the photographs.

Our research has been generously supported by the National Science Foundation under grant numbers DMC 84-51129, IRI 90-14490, and IRI 90-03986, nurtured especially by Howard Mora , the Army Research Office under grant DAAL88-K-0372 monitored by Jagdish Chandra, IBM, the AT&T Foundation, the GE Foundation, and HKUST under grant DAG 92/93 EG23. Our home institutions at UC Berkeley, the California Institute of Technology, and the Hong Kong University of Science and Technology have been exemplarily supportive of our e orts, providing the resources to help us to grow programs where there were none. We owe a special debt of gratitude in this regard to Karl Pister, Dean of Engineering at Berkeley until 1990.

The manuscript was classroom tested in various versions by James Clark at Harvard, John Canny, Curtis Deno and Matthew Berkemeier at Berkeley, and Joel Burdick at Caltech, in addition to the three of us. Their comments have been invaluable to us in revising the early drafts. We appreciate the detailed and thoughtful reviews by Greg Chirikjian of Johns Hopkins, and Michael McCarthy and Frank Park of the University of California, Irvine.

In addition, many students su ering early versions of this course have

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contributed to debugging the text. They include L. Bushnell, N. Getz, J.-P. Tennant, D. Tilbury, G. Walsh, and J. Wendlandt at Berkeley; R. Behnken, S. Kelly, A. Lewis, S. Sur, and M. van Nieuwstadt at Caltech; and A. Lee and J. Au of the Hong Kong University of Science and Technology. Sudipto Sur at Caltech helped develop a Mathematica package for screw calculus which forms the heart of the software described in Appendix B. We are ultimately indebted to these and the unnamed others for the inspiration to write this book.

Finally, on a personal note, we would like to thank our families for their support and encouragement during this endeavor.

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Chapter 1

Introduction

In the last twenty years, our conception and use of robots has evolved from the stu of science fiction films to the reality of computer-controlled electromechanical devices integrated into a wide variety of industrial environments. It is routine to see robot manipulators being used for welding and painting car bodies on assembly lines, stu ng printed circuit boards with IC components, inspecting and repairing structures in nuclear, undersea, and underground environments, and even picking oranges and harvesting grapes in agriculture. Although few of these manipulators are anthropomorphic, our fascination with humanoid machines has not dulled, and people still envision robots as evolving into electromechanical replicas of ourselves. While we are not likely to see this type of robot in the near future, it is fair to say that we have made a great deal of progress in introducing simple robots with crude end-e ectors into a wide variety of circumstances. Further, it is important to recognize that our impatience with the pace of robotics research and our expectations of what robots can and cannot do is in large part due to our lack of appreciation of the incredible power and subtlety of our own biological motor control systems.

1Brief History

The word robot was introduced in 1921 by the Czech playwright Karel Capek in his satirical play R. U. R. (Rossum’s Universal Robots), where he depicted robots as machines which resembled people but worked tirelessly. In the play, the robots eventually turn against their creators and annihilate the human race. This play spawned a great deal of further science fiction literature and film which have contributed to our perceptions of robots as being human-like, endowed with intelligence and even personality. Thus, it is no surprise that present-day robots appear primitive

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Figure 1.1: The Stanford manipulator. (Courtesy of the Coordinated Science Laboratory, University of Illinois at Urbana-Champaign)

when compared with the expectations created by the entertainment industry. To give the reader a flavor of the development of modern robotics, we will give a much abbreviated history of the field, derived from the accounts by Fu, Gonzalez, and Lee [35] and Spong and Vidyasagar [110]. We describe this roughly by decade, starting from the fifties and continuing up to the eighties.

The early work leading up to today’s robots began after World War II in the development of remotely controlled mechanical manipulators, developed at Argonne and Oak Ridge National Laboratories for handling radioactive material. These early mechanisms were of the master-slave type, consisting of a master manipulator guided by the user through a series of moves which were then duplicated by the slave unit. The slave unit was coupled to the master through a series of mechanical linkages. These linkages were eventually replaced by either electric or hydraulic powered coupling in “teleoperators,” as these machines are called, made by General Electric and General Mills. Force feedback to keep the slave manipulator from crushing glass containers was also added to the teleoperators in 1949.

In parallel with the development of the teleoperators was the devel-

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